Solving Absolute Value Inequalities & Compound Inequalities Worksheet | Algebra

A worksheet on solving inequalities with absolute values. Detailed solutions are included.

Master absolute value inequalities and compound modulus functions with this 4-page worksheet pack. Ideal for GCSE Further Maths, A-Level, and IB revision.

Help your students build a deep, structural understanding of inequalities and function boundaries with this printable Absolute Value (Modulus) Inequalities Worksheet Pack. Instead of just memorizing procedures, these exercises challenge learners to translate modulus inequality statements into compound logical steps and express their final solution sets clearly using interval notation.
This resource contains 2 student practice worksheets and 2 complete answer key pages—fully worked out to save you valuable marking time or to allow for student self-assessment!

Why Focus on Modulus Inequalities?
Understanding how to manipulate absolute value inequalities is a vital bridge between secondary algebra and advanced calculus. By training students to split absolute value bars into compound boundary inequalities (handling both greater than and less than conditions), they develop the precise algebraic reasoning required for high-tier exams.

What’s Included in This Resource?
• Worksheet 1: Basic & Multi-Step Modulus Inequalities: Students solve single absolute value statements involving greater than, less than, fractional expressions (such as x divided by 5), and multi-step distributions (like 4x minus 12 is less than or equal to 24).
• Worksheet 2: Compound Modulus Inequalities: Advanced problems featuring double boundaries (such as 3 is less than or equal to |3x - 6| which is less than 12) to challenge students’ critical thinking and intersection logic.
• Pages 3–4: Step-by-Step Answer Keys: Includes full solutions and structural breakdowns for every single question. Solutions are clearly mapped out showing the logical progression, set unions, and final answers in formal interval notation.

Curriculum and Age Suitability
• GCSE (Further / Upper Secondary): Highly relevant for higher-tier GCSE students, advanced Year 11 classes, and Further Maths students mastering coordinate geometry and advanced algebra.
• A-Level / IB Diploma: Excellent for Year 12 and Year 13 students as a transition resource, diagnostic tool, algebra intervention group resource, or formal exam revision.
• Adaptable Format: Perfect for whole-class lessons, independent desk work, secondary extensions, homework assignments, or structured test prep.